
This action transforms on-shell under any space-time transformation (REF ) as [1]}:
\(S[\mathbf {\Phi }]\rightarrow S^\prime [\mathbf {\tilde{\Phi }}]=S[\mathbf {\Phi }]+\int dt\int dx\text{ }\epsilon ^a\partial _\mu j^\mu _{\hspace{4.2679pt}a}(\mathbf {x})\) 
